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Chapter 13
355CHAPTER 13: QUADRATIC EQUATIONS AND APPLICATIONS
Chapter Objectives
By the end of this chapter, students should be able to: Apply the Square Root Property to solve quadratic equations Solve quadratic equations by completing the square and using the Quadratic Formula Solve applications by applying the quadratic formula or completing the squareContents
CHAPTER 13: QUADRATIC EQUATIONS AND APPLICATIONS .................................................................. 355
SECTION 13.1: THE SQUARE ROOT PROPERTY .................................................................................... 356
A. SOLVE BASIC QUADRATIC EQUATIONS USING SQUAREROOT PROPERTY ............................. 356B. ISOLATE THE SQUARED TERM .................................................................................................. 358
C. USE THE PERFECT SQUARE FORMULA ..................................................................................... 359
EXERCISE ........................................................................................................................................... 360
SECTION 13.2: COMPLETING THE SQUARE .......................................................................................... 361
A. COMPLETE THE SQUARE .......................................................................................................... 361
B. SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE, a = 1 .................................. 362C. SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE, A т 1 .................................. 363
EXERCISE ........................................................................................................................................... 365
SECTION 13.3: QUADRATIC FORMULA ................................................................................................ 366
A. DETERMINANT OF A QUADRATIC EQUATION ......................................................................... 366
B. APPLY THE QUADRATIC FORMULA .......................................................................................... 368
C.MAKE ONE SIDE OF AN EQUATION EQUAL TO ZERO .............................................................. 370
EXERCISE ........................................................................................................................................... 371
SECTION 13.4: APPLICATIONS WITH QUADRATIC EQUATIONS .......................................................... 372
A. PYTHAGOREAN THEOREM ....................................................................................................... 372
B.PROJECTILE MOTION ................................................................................................................ 373
C. COST AND REVENUE ................................................................................................................. 374
EXERCISE ........................................................................................................................................... 376
CHAPTER REVIEW ................................................................................................................................. 377
Chapter 13
356We might recognize a quadratic equation from the factoring chapter as a trinomial equation. Although,
it may seem that they are the same, but they aren't the same. Trinomial equations are equations with any
three terms. These terms can be any three terms where the degree of each can vary. On the other hand,
quadratic equations are equations with specific degree on each term.Definition
A quadratic equation is a polynomial equation of the formWhere ࢇ࢞
is called the leading term, ࢈࢞ is call the linear term, and ࢉ is called the constant coefficient
(or constant term). Additionally,SECTION 13.1: THE SQUARE ROOT PROPERTY
A. SOLVE BASIC QUADRATIC EQUATIONS USING SQUAREROOT PROPERTYSquare root property
Let ࢞ and ࢇ. Then = if and only if ࢞=±ξࢇIn other words,
=ࢇ if and only if ࢞=ξࢇ or ࢞= െξࢇMEDIA LESSON
Solve basic quadratic equations using square root property (Duration 2:53) View the video lesson, take notes and complete the problems belowExample:
a) 8ݔ =648 b) ݔ =75YOU TRY
Solve.
a) ݔ =81 b) ݔ =44Chapter 13
357MEDIA LESSON
Solve equations with even exponents (Duration 4:26) View the video lesson, take notes and complete the problems belowConsider: 5
= ________________ and (െ5) = ________________________ When we clear an even exponent, we have ________________________________________________.Example: Solve.
a) (5ݔെ1) = 49 =81YOU TRY
Solve.
a) (ݔ+4) =25 b) (6ݔെ9) =45Chapter 13
358B. ISOLATE THE SQUARED TERM
Let's look at examples where the leading term, or squared term, is not isolated. Recall, the squared term
must be isolated to apply the square root property.